Which model should I use to determine the similarity between predefined sentences and new sentences?
If this is a simple syntax comparison, neural networks is not the best way to achieve this.
If it's semantic comparison, then you can take a look at models used in the SNLI dataset for example.
From your question, it looks like just a syntax comparison.
Consider the 2 sentences :

She likes playing guitar
She likes listening guitar

The 2 sentences have almost the same words, but the meaning is different.
Now consider these 2 sentences :

The bird is taking a bath in the fountain
Birdie wash himself with water in public place

These 2 sentences have almost no words in common, but the meaning are very similar.

So if your use case need to return a high-score for the first example, give up neural network (it is possible, but pointless).
If your use case need to return a high-score in the second example, take a look at SNLI leaderboards, there is plenty of models that can works.